Question: Solve for $n$, $ \dfrac{3n + 1}{2n} = \dfrac{10}{10n} + \dfrac{6}{10n} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2n$ $10n$ and $10n$ The common denominator is $10n$ To get $10n$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{3n + 1}{2n} \times \dfrac{5}{5} = \dfrac{15n + 5}{10n} $ The denominator of the second term is already $10n$ , so we don't need to change it. The denominator of the third term is already $10n$ , so we don't need to change it. This give us: $ \dfrac{15n + 5}{10n} = \dfrac{10}{10n} + \dfrac{6}{10n} $ If we multiply both sides of the equation by $10n$ , we get: $ 15n + 5 = 10 + 6$ $ 15n + 5 = 16$ $ 15n = 11 $ $ n = \dfrac{11}{15}$